Sprint and T-Mobile said on Saturday that they had ended merger talks, marking the second time in three years that the two failed to reach a deal to create a stronger competitor to Verizon and AT&T.

The announcement represents a setback to Sprint, T-Mobile and their majority shareholders — Sprint is owned by the Japanese technology giant SoftBank and T-Mobile by Deutsche Telekom of Germany — in their efforts to create a stronger third-place competitor in the American wireless market.

But unlike three years ago, when Sprint and T-Mobile called off their last round of merger discussions because of strong opposition from the Barack Obama administration, this time the culprit was control.

The final blow to the latest round of talks came Saturday night in Tokyo, when Tim Höttges, the chief executive of Deutsche Telekom, met at the Tokyo home of SoftBank’s founder, Masayoshi Son, according to a person briefed on the matter. There, Mr. Höttges delivered to Mr. Son and Sprint’s chief executive, Marcelo Claure, new terms for a merger of the American companies.

Mr. Son and Mr. Claure ultimately rejected the plan because it did not give SoftBank and Sprint enough control over the combined entity, people briefed on the discussions said.

Choosing to abandon the deal talks means that Sprint and T-Mobile must now continue on their own paths to challenging their much bigger and better-financed rivals. For consumers, that probably signals a prolonging of a price war among the four wireless providers — one that analysts have said appears unsustainable for the smaller carriers in the long run.

In a joint statement, Sprint and T-Mobile said that they could not come to “mutually agreeable terms” for a combination.

“We have been clear all along that a deal with anyone will have to result in superior long-term value for T-Mobile’s shareholders compared to our outstanding stand-alone performance and track record,” John Legere, T-Mobile’s chief executive, said in the statement.

Mr. Claure of Sprint added in the statement, “We have agreed that it is best to move forward on our own.”

People briefed on the discussions, who spoke on condition of anonymity because they were not authorized to comment publicly, said that a deal always hinged on SoftBank’s comfort with taking a minority stake in the combined business. Deutsche Telekom was expected to be the biggest shareholder of the merged company, given that T-Mobile is the bigger business by market value. T-Mobile’s market capitalization as of Friday’s close was $48.5 billion, while Sprint’s was $26.7 billion.

Though the two had been in on-again, off-again talks for months, they appeared to be making progress, with an eye on striking a deal before Thanksgiving. But at a SoftBank board meeting on Friday, several directors of the Japanese company expressed reservations about giving up control of a major telecom service provider, according to one of the people briefed on the matter.

Image

A T-Mobile store in New York. The end of the merger talks between T-Mobile and Sprint marked the second time in three years that the two have failed to reach a deal.CreditAmr Alfiky/Reuters

Shares in both companies fell last week after Nikkei Asian Review, a Japanese business publication, reported that SoftBank intended to walk away from the transaction. But Deutsche Telekom and T-Mobile planned to make one last offer to SoftBank and Sprint.

The stakes for Sprint and T-Mobile are perhaps higher now than they were in the summer of 2014, when the two last pursued a merger. While both have waged a price war against their bigger competitors, drawing new customers in the process, few in the industry believe that the Sprint and T-Mobile can sustain the costs of a drawn-out war against better-capitalized opponents.

Walking away from a merger with T-Mobile will provide the biggest test yet of Mr. Son’s ability to turn around Sprint after more than a decade of trouble. The billionaire led SoftBank’s takeover of the troubled American telecom in 2012, paying nearly $22 billion for a majority stake.

At the time, Mr. Son argued that he could take on Verizon and AT&T — but those ambitions hinged on ultimately combining his new telecom with T-Mobile. Then, Sprint was seen as the stronger company and in position to own a bigger share of the combined business.

Three years later, however, T-Mobile has become the better performer, its brash cost-cutting campaign forced Verizon and AT&T into a tough price war. Sprint has largely lagged behind, though analysts praised its third-quarter financial performance as showing signs of promise.

Putting the two companies together would have created a business with more scale — and more financial capability to pay for both network upgrades and discounts for service plans.

Sprint, in particular, was seen as bearing a bigger financial burden, carrying $34.2 billion in long-term debt on its books as of Sept. 30, while having posted annual losses for years. T-Mobile, while reporting $27.7 billion in long-term debt as of Sept. 30, has been profitable every year since 2013.

Combining the two telecom providers would have helped their majority shareholders as well. SoftBank has faced concerns from investors about how it would manage Sprint’s debt load, while Deutsche Telekom has been concerned about the fate of its best-performing business asset.

Among the most prominent advocates of a merger of the two companies was Mr. Son of SoftBank. “Three is a real fight, a real competition,” he said in a Bloomberg Television interview in September.

Both companies had been hoping that, unlike in 2014, a merger of the two would be looked upon more favorably this time around. The Obama administration had strongly hinted that it would fight to oppose a merger of Sprint and T-Mobile, arguing that consolidation would hurt consumers. By contrast, the deal makers at both companies said that they believed the Trump administration would let a deal take place.

Now, Sprint and T-Mobile will be left on their own to battle Verizon and AT&T — and each other. Executives from both companies appeared ready to wage that fight.

“We are determined to continue our efforts to change the wireless industry and compete fiercely,” Mr. Claure said in the joint statement. “We look forward to continuing to take the fight to the duopoly and newly emerging competitors.”

And Mr. Legere wrote in a tweet, “We’ve been changing this industry for good for the past 5 years and #WeWontStop!”

A version of this article appears in print on , on Page A27 of the New York edition with the headline: Sprint and T-Mobile End Merger Talks Once Again. Order Reprints | Today’s Paper | Subscribe